please check my working, trig indentity proof

**Tweety** · December 14th 2009, 03:34 AM

Can someome please check my working and tell me if it is 'correct'. As my book shows a different method.

using $cos2A = 2cos^{2}A - 1 = 1-2sin^{2}A$

show that; $cos^{2}\frac{x}{2} = \frac{1+cosx}{2}$

my method;

$cosx = cos2\frac{x}{2} = 2cos^{2}\frac{x}{2}-1$

$\frac{1+ 2cos^{2}\frac{x}{2}-1}{2}$ The one's cancel, and I get

$\frac{2cos^{2}\frac{x}{2}}{2}$

and now can I cancel the two's to give me

$cos^{2}\frac{x}{2}$

or do I have to cancel both 'two's at the top?

thanks

**Prove It** · December 14th 2009, 04:10 AM

Originally Posted by Tweety

Can someome please check my working and tell me if it is 'correct'. As my book shows a different method.

using $cos2A = 2cos^{2}A - 1 = 1-2sin^{2}A$

show that; $cos^{2}\frac{x}{2} = \frac{1+cosx}{2}$

my method;

$cosx = cos2\frac{x}{2} = 2cos^{2}\frac{x}{2}-1$

$\frac{1+ 2cos^{2}\frac{x}{2}-1}{2}$ The one's cancel, and I get

$\frac{2cos^{2}\frac{x}{2}}{2}$

and now can I cancel the two's to give me

$cos^{2}\frac{x}{2}$

or do I have to cancel both 'two's at the top?

thanks

You got to $\cos{2\left(\frac{x}{2}\right)} = 2\cos^{2}\frac{x}{2}-1$

$\cos{x} = 2\cos^2{\frac{x}{2}} - 1$

$\cos{x} + 1 = 2\cos^2{\frac{x}{2}}$

$\frac{\cos{x} + 1}{2} = \cos^2{\frac{x}{2}}$ .

**Tweety** · December 14th 2009, 04:47 AM

Originally Posted by Prove It

You got to $\cos{2\left(\frac{x}{2}\right)} = 2\cos^{2}\frac{x}{2}-1$

$\cos{x} = 2\cos^2{\frac{x}{2}} - 1$

$\cos{x} + 1 = 2\cos^2{\frac{x}{2}}$

$\frac{\cos{x} + 1}{2} = \cos^2{\frac{x}{2}}$ .

Thanks, I understand what you did, however I dont quite understand what I did wrong?

could you please show/point out to me? cause both methods 'looks' valid to me, is it the last part where I cancel 2?

thanks.

**Grandad** · December 14th 2009, 08:01 AM

Hello Tweety

Originally Posted by Tweety

Thanks, I understand what you did, however I dont quite understand what I did wrong?

could you please show/point out to me? cause both methods 'looks' valid to me, is it the last part where I cancel 2?

thanks.

There's nothing wrong with your original method. You cancelled the 2's correctly.

Grandad

**Tweety** · December 14th 2009, 08:22 AM

Thanks.

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